Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Bychkov, Boris"'
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
We use the theory of $x-y$ duality to propose a new definition / construction for the correlation differentials of topological recursion; we call it "generalized topological recursion". This new definition coincides with the original topological recu
Externí odkaz:
http://arxiv.org/abs/2408.02608
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
We prove that for any initial data on a genus zero spectral curve the corresponding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type form
Externí odkaz:
http://arxiv.org/abs/2406.07391
Publikováno v:
Journal of Geometry and Physics, V.207 (2024)
In this paper we relate a well-known in symplectic geometry compactification of the space of symmetric bilinear forms considered as a chart of the Lagrangian Grassmannian to the specific compactifications of the space of electrical networks in the di
Externí odkaz:
http://arxiv.org/abs/2406.03021
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log topological
Externí odkaz:
http://arxiv.org/abs/2405.10720
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
Publikováno v:
Int. Math. Res. Not. IMRN 2024, no. 21, 13461--13487
We introduce a new concept of logarithmic topological recursion that provides a patch to topological recursion in the presence of logarithmic singularities and prove that this new definition satisfies the universal $x-y$ swap relation. This result pr
Externí odkaz:
http://arxiv.org/abs/2312.16950
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
We discuss a universal relation that we call the $x-y$ swap relation, which plays a prominent role in the theory of topological recursion, Hurwitz theory, and free probability theory. We describe in a very precise and detailed way the interaction of
Externí odkaz:
http://arxiv.org/abs/2309.12176
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
Publikováno v:
J. Geom. Phys. 206 (2024), 105329, 13 pp
For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the $n$-point functions produced by the topological recursion on these curves via the $n$-point functions on the or
Externí odkaz:
http://arxiv.org/abs/2304.11687
Autor:
Alexandrov, Alexander, Bychkov, Boris, Dunin-Barkowski, Petr, Kazarian, Maxim, Shadrin, Sergey
We prove a recent conjecture of Borot et al. that a particular universal closed algebraic formula recovers the correlation differentials of topological recursion after the swap of $x$ and $y$ in the input data. We also show that this universal formul
Externí odkaz:
http://arxiv.org/abs/2212.00320
We consider weighted double Hurwitz numbers, with the weight given by arbitrary rational function times an exponent of the completed cycles. Both special singularities are arbitrary, with the lengths of cycles controlled by formal parameters (up to s
Externí odkaz:
http://arxiv.org/abs/2206.14792
We refine the result of T. Lam \cite{L} on embedding the space $E_n$ of electrical networks on a planar graph with $n$ boundary points into the totally non-negative Grassmannian $\mathrm{Gr}_{\geq 0}(n-1,2n)$ by proving first that the image lands in
Externí odkaz:
http://arxiv.org/abs/2109.13952